The function fx=x−12+(x−2)2+(x−3)2+…+(x−9)2 has minimum value at x =

f(x)=(x−1)2+(x−2)2+……+(x−9)2 f1(x)=2(x−1)+2(x−2)+……+2(x−9) f1(x)=0 9x−45=0 x=5 f11(x)=18>0f(x)has minimum atx=5.

The function fx=x−12+(x−2)2+(x−3)2+…+(x−9)2 has minimum value at x =

f(x)=(x−1)2+(x−2)2+……+(x−9)2 f1(x)=2(x−1)+2(x−2)+……+2(x−9) f1(x)=0 9x−45=0 x=5 f11(x)=18>0f(x)has minimum atx=5.

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The function $f (x) = {(x - 1)}^{2} +$ $(x - 2)^{2} + (x - 3)^{2} + \dots + (x - 9)^{2}$ has minimum value at x =

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answer is C.

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Detailed Solution

$\begin{aligned} f (x) = (x - 1)^{2} + (x - 2)^{2} + \dots \dots + (x - 9)^{2} \\ f^{1} (x) = 2 (x - 1) + 2 (x - 2) + \dots \dots + 2 (x - 9) \end{aligned}$
$\begin{aligned} f^{1} (x) = 0 \\ 9 x - 45 = 0 \\ x = 5 \\ f^{11} (x) = 18 > 0 \end{aligned}$
$f (x) has minimum at x = 5 .$